In an election between two candidates, the candidate who gets 40% of the total votes is defeated by 1,600 votes. The total number of votes polled is:
Correct answer: (D) 8,000.
The total number of votes polled was 8,000, because the 1,600-vote margin equals 20% of the total votes.
Explanation
In a two-candidate election, if one candidate receives 40% of the total votes, the other receives the remaining 60%. The defeat margin is therefore the difference between their vote shares: 60% - 40% = 20% of the total. Britannica explains percentage as a value expressed in hundredth parts of a quantity, with the relation x = PT/100 linking a percentage to the total reference quantity. Here, 20% of the total equals 1,600 votes, so the total is 1,600 x 100/20 = 8,000. This is why option D matches the given margin exactly.
Why the other options are wrong
- (A) If the total were 12,000, the 20% gap between 60% and 40% would be 2,400 votes, not 1,600.
- (B) If the total were 10,000, the losing candidate's 40% share would be 4,000 and the winner's 60% share would be 6,000, giving a 2,000-vote margin.
- (C) If the total were 6,000, the 20% difference would be only 1,200 votes, so it cannot produce the stated defeat margin.
Concept
This tests percentage-to-total conversion in Reasoning & Mental Ability: a known percentage difference is used to recover the 100% base. It recurs in RAS-style arithmetic because comparison problems often hide the total behind two shares of the same quantity.